The problem asks to convert $225^{\circ}$ to radians.

1. Problem Description

The problem asks to convert $225^{\circ}$ to radians.

2. Solution Steps

To convert degrees to radians, we use the following formula:

$radians = degrees \times \frac{\pi}{180}$

Plugging in the given value:

$radians = 225 \times \frac{\pi}{180}$

We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor. The greatest common divisor of 225 and 180 is

4

5. $225 = 45 \times 5$

$180 = 45 \times 4$

So,

$radians = \frac{225}{180}\pi = \frac{45 \times 5}{45 \times 4}\pi = \frac{5}{4}\pi$

$radians = \frac{5\pi}{4}$

3. Final Answer

$\frac{5\pi}{4}$